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- Question 1 is worth 4 points. Questions 2 and 3 are worth 9 points each.
- A card is drawn from a deck. Find the probability that the card is:
- an ace
- a heart
- the 2 of clubs
- a 7 or a spade
 A slot machine has three spinning cylinders. The first cylinder contains four symbols including a 7. The second has five symbols including a 7. And the third cylinder has six symbols including a 7.
On one pull, what is the probability:
- you will get three 7s.
- the only 7 occurs on the left.
- you will get exactly two 7s.
In the die rolling experiment, we surveyed how many die rolls were needed in order to roll a one. Find the probability that it takes:
- two tries
- five tries
- n tries
Questions 4-9 are worth 8 points each.
![dice]() Two dice are rolled. Find the probability that:
- the sum of the dice is 6
- the sum of the dice is 11
- both dice land on the same number
- both dice land on odd numbers
A box contains 3 red marbles, 2 green marbles, and 5 blue marbles. Three marbles are randomly removed from the box. Find the probability that:
- the first marble is red
- all three marbles are red
- none of the marbles are red
- the first marble is red, the second is blue, and the third is green
A fair coin is flipped three times, and we want to find the probability that the coin lands on a head exactly twice. By drawing the sample space we can see that 3 of the 8 possible outcomes contain exactly two heads.
 HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
Therefore, the probability is 3/8. In general:
| For 3 flips: |
P[zero heads] = 1/8
P[one head] = 3/8
P[two heads] = 3/8
P[three heads] = 1/8 |
For 4 flips: |
P[zero heads] = 1/16
P[one head] = 4/16
P[two heads] = 6/16
P[three heads] = 4/16
P[four heads] = 1/16 |
Consider a coin that is flipped 5 times. Use Pascal's Triangle to figure out the probability that the number of heads that occur is exactly:
- zero
- one
- two
- three
- four
- five
White Cars
An automobile manufacturer has three factories, A, B, and C. They produce 50%, 30%, and 20%, respectively, of a specific model of car. Thirty percent of the cars produced in factory A are white, 40% of those produced in factory B are white, and 25% produced in factory C are white. If an automobile produced by the company is selected at random, find the probability that it is white.
Eight Kids
A woman has eight children. What is the probability that at least one of them is a girl? (Assume that the probability of having a boy is the same as the probability of having a girl.)
Let's Make A Deal
You are a contestant on the game show "Let's Make A Deal." There are three curtains. Behind two of the curtains are goats and behind the third is a new car. You are told to choose a curtain. You will get to keep whatever is behind it. After making your choice, the host says, "I shall now open one of the other curtains and show you a goat," which he does. The host then gives you the choice of keeping with your first pick or switching to the other unopened curtain. Should you switch? Why or why not?
The Penny Flipping Game
Three people are playing a game. They take turns flipping a penny. The first person to get a head wins and the game ends. If no one has won after each has flipped, they start again in the same order. (It is possible that a large number of flips may be required before a winner can be determined.) What is the probability that the person that flips first wins the game? (15 points)
Amoebae
A jar begins with one amoeba. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with probability 25% for each case. What is the probability that the amoeba population eventually dies out? (15 points)
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- BONUS QUESTION: Coinciding Birthdays
What is the minimum number of randomly chosen people needed so that there is at least a 50% chance that at least two have the same birthday? (10 points)
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